Continuous Time Formulation and Lagrangian Relaxation Algorithm for the Gate Assignment Problem

Algorithm 2

Step 1. Exchange between the apron and gates. Sequence the flights assigned to the apron by nondecreasing order with the arrival time. For each flight in the sequence, check if it can be exchanged with any flight that is assigned to the gates. If so, calculate the objective value obtained after exchanging the flights, and execute the exchange that leads to the minimum objective function; if not, continue to check the next flight assigned to the apron until all the flights have been checked.

Step 2. Exchange among the gates. Sequence the flights assigned to the gates by nondecreasing order with the arrival time. For each flight in the sequence, check if it can be exchanged with any flight that is assigned to other gates. If so, calculate the objective value obtained after exchanging the flights and execute the exchange that leads to the minimum objective function; if not, continue to check the next flight assigned to the gates until all the flights have been checked.